Quantum state transformations and the Schubert calculus
arXiv:quant-ph/0410052 · doi:10.1016/j.aop.2004.09.012
Abstract
Recent developments in mathematics have provided powerful tools for comparing the eigenvalues of matrices related to each other via a moment map. In this paper we survey some of the more concrete aspects of the approach with a particular focus on applications to quantum information theory. After discussing the connection between Horn's Problem and Nielsen's Theorem, we move on to characterizing the eigenvalues of the partial trace of a matrix.
40 pages. Accepted for publication in Annals of Physics